This paper presents the development of an efficient finite element model for the analysis of laminated composite beams treated by a constrained viscoelastic layer. The formulation presented includes the ability to model a structure about preloaded configurations. Since most of the damping ability is due to the shearing of the viscoelastic layer, the model is designed to represent this aspect accurately. An offset beam, shear-deformable element, which is specially suited for modeling such laminated beams is presented. The viscoelastic layer is modeled by using two-dimensional plane finite elements which are compatible with the beam elements. In case of a structure with initial load, the final equations are linearized so that first increment of motion, the part due to the initial load is linear, and the second, the part due to the dynamic load is linearized. System damping and tip displacement are compared with existing approximate results and experimental data whenever possible. Results confirm that dynamic response is substantially improved by use of such damping treatments, and give some useful information regarding designing a structure for high damping using constrained damping treatments.